The perturbative scales entering the calculation are defined according to
the CKKW-style scale setting prescription [1]}, [2]}.
In this procedure the hard-process partons are clustered into a Born-like
\(2\rightarrow 2\)  configuration that defines the core process with an associated
scale \(\mu _{\text{core}}\) . For the production channels considered here the event-wise
determined core process, of order \(\alpha _\text{s} ^{n_{\text{core}}}\) , can correspond
to \(jj\rightarrow \mu ^+\mu ^-\)  (\(n_{\text{core}}=0\) ), \(jj\rightarrow Zj\)  (\(n_{\text{core}}=1\) ),
or \(jj\rightarrow jj\)  (\(n_{\text{core}}=2\) ). For the three possible cluster configurations
the corresponding core-process scale is given by
\(\mu _{\text{core}}=\mathopen {}\mathclose {\left\lbrace \begin{array}{lcl}m_{\mu ^+\mu ^-} &:& n_{\text{core}}=0\\\sqrt{m^2_{\mu ^+\mu ^-}+p^2_{T,\mu ^+\mu ^-}} &:& n_{\text{core}}=1\;.\\p_{T,j} &:& n_{\text{core}}=2\end{array}\right.}\) 
